Investigating Preservice Teachers’ Interpretations and Discussion of Real-Life Examples: Focusing on the Use of Percent

Ji-Eun Lee 1, Sunghwan Hwang 2 *
More Detail
1 Teacher Development and Educational Studies, Oakland University, Rochester, MI, USA
2 Department of Elementary Mathematics Education, Seoul National University of Education, Seoul, SOUTH KOREA
* Corresponding Author
EUR J SCI MATH ED, Volume 10, Issue 3, pp. 324-337. https://doi.org/10.30935/scimath/11917
Published: 24 March 2022
OPEN ACCESS   962 Views   552 Downloads
Download Full Text (PDF)

ABSTRACT

The objective of this study is to examine the characteristics of PSTs’ selection of real-life examples for discussion, the aspects they attended to during the discussion, and their reflection on facilitating the discussion. A total of 46 elementary PSTs in the US joined in the study. We gathered data from a three-phase task using an online course management platform and restricted the real-life contexts using percent. The collected data were analyzed using enumerative and ethnographic content analysis. The findings revealed that while we detected some shifting features in PSTs’ selection of real-life contexts compared to prior studies, we found their static preference of contexts around consumer practices over others (e.g., contexts related to science and critical literacy). The findings also revealed that PSTs tended to pay attention to the contexts with critical views when the context was not straightforward and direct computations were not readily feasible to get the final answer. Moreover, the vague contexts helped encourage PSTs to view the situations critically, but they had difficulties having meaningful mathematical discussions in such contexts. We provided suggestions and implications for future research based on these findings.
Keywords: preservice elementary school teachers, real-life examples, teacher interpretation, group discussion, percent

CITATION

Lee, J.-E., & Hwang, S. (2022). Investigating Preservice Teachers’ Interpretations and Discussion of Real-Life Examples: Focusing on the Use of Percent. European Journal of Science and Mathematics Education, 10(3), 324-337. https://doi.org/10.30935/scimath/11917

REFERENCES

  • Altay, M. K., Yalvac, B., & Yeltekin, E. (2017). 8th grade student’s skill of connecting mathematics to real life. Journal of Education and Training Studies, 5(10), 158-166. https://doi.org/10.11114/jets.v5i10.2614
  • Beswick, K. (2011). Putting context in context: An examination of the evidence for the benefits of “contextualised” tasks. International Journal of Science and Mathematics Education, 9(2), 367-390. https://doi.org/10.1007/s10763-010-9270-z
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 73-96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9
  • Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects: State, trends and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/bf00302716
  • Bolstad, O. H. (2020). Secondary teachers’ operationalisation of mathematical literacy. European Journal of Science and Mathematics Education, 8(3), 115-135. https://doi.org/10.30935/scimath/9551
  • Bruner, J. (1985). Narrative and paradigmatic modes of thought. In E. Eisner (Ed.), Learning and teaching the ways of knowing (pp. 97-115). University of Chicago Press. https://doi.org/10.1177/016146818508600606
  • Chapman, O. (2006). Classroom practices for context of mathematics word problems. Educational Studies in Mathematics, 62(2), 211-230. https://doi.org/10.1007/s10649-006-7834-1
  • de Lange Jnz, J. (1996). Using and applying mathematics in education. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of mathematics education (pp. 49-97). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-1465-0_4
  • DeCuir-Gunby, J. T., Marshall, P. L., & McCulloch, A. W. (2011). Developing and using a codebook for the analysis of interview data: An example from a professional development research project. Field Methods, 23(2), 136-155. https://doi.org/10.1177/1525822X10388468
  • Depaepe, F., De Corte, E., & Verschaffel, L. (2010). Teachers’ approaches towards word problem solving: Elaborating or restricting the problem context. Teaching and Teacher Education, 26(2), 152-160. https://doi.org/10.1016/j.tate.2009.03.016
  • Ensign, J. (2005). Helping teachers use students’ home cultures in mathematics lessons: Developmental stages of becoming effective teachers of diverse students. In A. J. Rodriguez, & R. S. Kitchen (Eds.), Preparing mathematics and science teachers for diverse classrooms: Promising strategies for transformative pedagogy (pp. 225-242). Erlbaum.
  • Ernest, P. (2016). Mathematics and values. In B. Larvor (Ed.), Mathematical cultures (pp. 189-214). Birkhäuser. https://doi.org/10.1007/978-3-319-28582-5_12
  • Freudenthal, H. (1968). Why to teach mathematics so as to be useful. Educational Studies in Mathematics, 1(2), 3-8. https://doi.org/10.1007/bf00426224
  • Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic Publishers.
  • Gainsburg, J. (2009). How and why secondary mathematics teachers make (or don’t make) real-world connections in teaching. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 265-281). Sense Publishers. https://doi.org/10.1163/9789087909383_017
  • Garii, B., & Okumu, L. (2008). Mathematics and the world: What do teachers recognize as mathematics in real world practice? The Mathematics Enthusiast, 5(2), 291-304. https://doi.org/10.54870/1551-3440.1108
  • Gellert, U., & Jablonka, E. (2009). “I am not talking about reality”: Word problems and the intricacies of producing legitimate text. In L. Verschaffel, B. Greer, W. Van Dooren, & S. Mukhopadhyay (Eds.), Words and worlds: Modelling verbal descriptions of situations (pp. 39-53). Sense Publishers. https://doi.org/10.1163/9789087909383_004
  • Ghousseini, H., & Herbst, P. (2016). Pedagogies of practice and opportunities to learn about classroom mathematics discussions. Journal of Mathematics Teacher Education, 19(1), 79-103. https://doi.org/10.1007/s10857-014-9296-1
  • González, G. (2017). Teachers’ understandings of realistic contexts to capitalize on students’ prior knowledge. School Science and Mathematics, 117(7-8), 329-340. https://doi.org/10.1111/ssm.12249
  • Grbich, C. (2013). Qualitative data analysis: An introduction. SAGE. https://doi.org/10.4135/9781529799606
  • Greer, B. (1997). Modelling reality in mathematics classrooms: The case of word problems. Learning and Instruction, 7(4), 293-307. https://doi.org/10.1016/s0959-4752(97)00006-6
  • Inoue, N. (2005). The realistic reasons behind unrealistic solutions: The role of interpretive activity in word problem solving. Learning and Instruction, 15(1), 69-83. https://doi.org/10.1016/j.learninstruc.2004.12.004
  • Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How does realistic mathematics education (RME) improve students’ mathematics cognitive achievement? Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569-578. https://doi.10.12973/ejmste/76959
  • Lee, J.-E. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 15(6), 429-452. https://doi.org/10.1007/s10857-012-9220-5
  • Mason, J. (2016). When is a problem? When is actually the problem? In P. Felmer, E. Pehkonen, & J. Kilpatrick (Eds.), Posing and solving mathematical problems: Advances and new perspectives (pp. 263-285). Springer. https://doi.org/10.1007/978-3-319-28023-3_16
  • National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common core state standards for mathematics. NGA & CCSSO. http://www.corestandards.org/about-the-standards/branding-guidelines/
  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education. https://files.eric.ed.gov/fulltext/ED500486.pdf
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. https://www.nctm.org/standards/
  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. https://www.nctm.org/Store/Products/Principles-to-Actions--Ensuring-Mathematical-Success-for-All/
  • Organisation for Economic Co-operation and Development. (2019). PISA 2018 assessment and analytical framework. OECD publishing. https://www.oecd-ilibrary.org/education/pisa-2018-assessment-and-analytical-framework_b25efab8-en
  • Pirasa, N. (2016). The connection competencies of pre-service mathematics teachers about geometric concepts to daily-life. Universal Journal of Educational Research, 4(12), 2840-2851. https://doi.org/10.13189/ujer.2016.041218
  • Pöhler, B., George, A. C., Prediger, S., & Weinert, H. (2017). Are word problems really more difficult for students with low language proficiency? Investigating percent items in different formats and types. International Electronic Journal of Mathematics Education, 12(3), 667-687. https://doi.org/10.29333/iejme/641
  • Popovic, G., & Lederman, J. S. (2015). Implications of informal education experiences for mathematics teachers’ ability to make connections beyond formal classroom. School Science and Mathematics, 115(3), 129-140. https://doi.org/10.1111/ssm.12114
  • Rubel, L. H., & McCloskey, A. V. (2021). Contextualization of mathematics: Which and whose world. Educational Studies in Mathematics, 107, 383-404. https://doi.org/10.1007/s10649-021-10041-4
  • Simic-Muller, K., & Fernandes, A. (2020). Preservice teachers’ understanding of ‘real world’: Developing a typology. MERGA International Journal for Mathematics Teaching and Learning, 21(1), 31-53.
  • Solomon, Y., Hough, S., & Gough, S. (2021). The role of appropriation in guided reinvention: Establishing and preserving devolved authority with low-attaining students. Educational Studies in Mathematics, 106(2), 171-188. https://doi.10.1007/s10649-020-09998-5
  • Strauss, A., & Corbin, J. (1990). Basics of qualitative research. SAGE. https://doi.org/10.4135/9781452230153
  • TeachingWorks. (n. d.). High-leverage content. http://www.teachingworks.org/work-of-teaching/high-leverage-content
  • van de Walle, J., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally. Pearson.
  • Verschaffel, L., De Corte, E., & Borghart, I. (1997). Pre-service teachers’ conceptions and beliefs about the role of real-world knowledge in mathematical modelling of school word problems. Learning and Instruction, 7(4), 339-359. https://doi.org/10.1016/s0959-4752(97)00008-x
  • Watson, A. (2004). Red herrings: Post-14 ‘best’ mathematics teaching and curricula. British Journal of Educational Studies, 52(4), 359-376. https://doi.org/10.1111/j.1467-8527.2004.00273.x
  • Yilmaz, R. (2020). Prospective mathematics teachers’ cognitive competencies on realistic mathematics education. Journal on Mathematics Education, 11(1), 17-44. https://doi.org/10.22342/jme.11.1.8690.17-44